Quantitative Reasoning: Geometry and Measurement Flashcards

A cylindrical container of disinfectant has a radius of 3 cm and a height of 10 cm. What is its volume?

Answer: 90π cm³

V = πr²h = π × 9 × 10 = 90π cm³.

What is the distance between the points (1, 2) and (7, 10) on a coordinate plane?

Answer: 10

Distance = √((7−1)² + (10−2)²) = √(36 + 64) = √100 = 10.

A dental office orders 3 gallons of distilled water. How many quarts is this?

Answer: 12 quarts

There are 4 quarts in a gallon, so 3 × 4 = 12 quarts.

A trapezoid has parallel bases of 8 cm and 12 cm and a height of 5 cm. What is its area?

Answer: 50 cm²

Area = ½(8 + 12) × 5 = 10 × 5 = 50 cm².

Triangle A has sides 3, 4, and 5. Triangle B is similar, and its side corresponding to 3 measures 9. What is the longest side of Triangle B?

Answer: 15

The scale factor is 9 ÷ 3 = 3, so the longest side is 5 × 3 = 15.

A circle has a circumference of 12π inches. What is its area?

Answer: 36π in²

C = 2πr gives r = 6, so area = π × 6² = 36π in².

Given that 1 inch = 2.54 cm, approximately how many inches long is a 10 cm instrument?

Answer: 3.94 in

10 ÷ 2.54 ≈ 3.94 inches.